There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Molecular self-assembly is the spontaneous association of molecules under equilibrium conditions into stable, structurally well-defined aggregates joined by noncovalent bonds. Molecular self-assembly is ubiquitous in biological systems and underlies the formation of a wide variety of complex biological structures. Understanding self-assembly and the associated noncovalent interactions that connect complementary interacting molecular surfaces in biological aggregates is a central concern in structural biochemistry. Self-assembly is also emerging as a new strategy in chemical synthesis, with the potential of generating nonbiological structures with dimensions of 1 to 10(2) nanometers (with molecular weights of 10(4) to 10(10) daltons). Structures in the upper part of this range of sizes are presently inaccessible through chemical synthesis, and the ability to prepare them would open a route to structures comparable in size (and perhaps complementary in function) to those that can be prepared by microlithography and other techniques of microfabrication.

Molecular self-assembly and nanochemistry: A chemical strategy for the synthesis of nanostructures

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

The electronic properties and relatively small size of fluorine endow it with considerable versatility as a bioisostere and it has found application as a substitute for lone pairs of electrons, the hydrogen atom, and the methyl group while also acting as a functional mimetic of the carbonyl, carbinol, and nitrile moieties. In this context, fluorine substitution can influence the potency, conformation, metabolism, membrane permeability, and P-gp recognition of a molecule and temper inhibition of the hERG channel by basic amines. However, as a consequence of the unique properties of fluorine, it features prominently in the design of higher order structural metaphors that are more esoteric in their conception and which reflect a more sophisticated molecular construction that broadens biological mimesis. In this Perspective, applications of fluorine in the construction of bioisosteric elements designed to enhance the in vitro and in vivo properties of a molecule are summarized.

Fluorine and Fluorinated Motifs in the Design and Application of Bioisosteres for Drug Design.

Markov state models of molecular kinetics (MSMs), in which the long-time statistical dynamics of a molecule is approximated by a Markov chain on a discrete partition of configuration space, have seen widespread use in recent years. This approach has many appealing characteristics compared to straightforward molecular dynamics simulation and analysis, including the potential to mitigate the sampling problem by extracting long-time kinetic information from short trajectories and the ability to straightforwardly calculate expectation values and statistical uncertainties of various stationary and dynamical molecular observables. In this paper, we summarize the current state of the art in generation and validation of MSMs and give some important new results. We describe an upper bound for the approximation error made by modeling molecular dynamics with a MSM and we show that this error can be made arbitrarily small with surprisingly little effort. In contrast to previous practice, it becomes clear that the best MSM is not obtained by the most metastable discretization, but the MSM can be much improved if non-metastable states are introduced near the transition states. Moreover, we show that it is not necessary to resolve all slow processes by the state space partitioning, but individual dynamical processes of interest can be resolved separately. We also present an efficient estimator for reversible transition matrices and a robust test to validate that a MSM reproduces the kinetics of the molecular dynamics data.

/pdf/markov-models-of-molecular-kinetics-generation-and-rcn40bw5dw.pdf

Markov models of molecular kinetics: Generation and validation

Multivalent interactions can be applied universally for a targeted strengthening of an interaction between different interfaces or molecules. The binding partners form cooperative, multiple receptor-ligand interactions that are based on individually weak, noncovalent bonds and are thus generally reversible. Hence, multi- and polyvalent interactions play a decisive role in biological systems for recognition, adhesion, and signal processes. The scientific and practical realization of this principle will be demonstrated by the development of simple artificial and theoretical models, from natural systems to functional, application-oriented systems. In a systematic review of scaffold architectures, the underlying effects and control options will be demonstrated, and suggestions will be given for designing effective multivalent binding systems, as well as for polyvalent therapeutics.

Multivalency as a chemical organization and action principle.

Robust Perron cluster analysis in conformation dynamics

Given a row-stochastic matrix describing pairwise similarities between data objects, spectral clustering makes use of the eigenvectors of this matrix to perform dimensionality reduction for clustering in fewer dimensions. One example from this class of algorithms is the Robust Perron Cluster Analysis (PCCA+), which delivers a fuzzy clustering. Originally developed for clustering the state space of Markov chains, the method became popular as a versatile tool for general data classification problems. The robustness of PCCA+, however, cannot be explained by previous perturbation results, because the matrices in typical applications do not comply with the two main requirements: reversibility and nearly decomposability. We therefore demonstrate in this paper that PCCA+ always delivers an optimal fuzzy clustering for nearly uncoupled, not necessarily reversible, Markov chains with transition states.

Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification

Indiscriminate activation of opioid receptors provides pain relief but also severe central and intestinal side effects. We hypothesized that exploiting pathological (rather than physiological) conformation dynamics of opioid receptor-ligand interactions might yield ligands without adverse actions. By computer simulations at low pH, a hallmark of injured tissue, we designed an agonist that, because of its low acid dissociation constant, selectively activates peripheral μ-opioid receptors at the source of pain generation. Unlike the conventional opioid fentanyl, this agonist showed pH-sensitive binding, heterotrimeric guanine nucleotide–binding protein (G protein) subunit dissociation by fluorescence resonance energy transfer, and adenosine 3′,5′-monophosphate inhibition in vitro. It produced injury-restricted analgesia in rats with different types of inflammatory pain without exhibiting respiratory depression, sedation, constipation, or addiction potential.

https://science.sciencemag.org/content/sci/355/6328/966.full.pdf

A nontoxic pain killer designed by modeling of pathological receptor conformations

Multivalente Wechselwirkungen konnen universell zur gezielten Bindungsverstarkung zwischen verschiedenen Grenzflachen oder Molekulen genutzt werden. Die Bindungspartner bilden dabei kooperativ multiple Rezeptor-Ligand-Wechselwirkungen, die auf einzelnen schwachen, nichtkovalenten Bindungen basieren und daher prinzipiell reversibel sind. Daher spielen multi- und polyvalente Wechselwirkungen in biologischen Systemen eine entscheidende Rolle fur Erkennungs-, Adhasions- und Signalprozesse. Die wissenschaftliche und praktische Etablierung dieses Prinzips wird anhand der Entwicklung von naturlichen Systemen uber einfache artifizielle und theoretische Modelle hin zu anwendungsorientierten funktionalen Systemen demonstriert. Anhand eines systematischen Uberblicks uber Gerustarchitekturen werden die zugrunde liegenden Wirk- und Steuerungsmoglichkeiten aufgezeigt und Designvorschlage fur moglichst effektive multivalente Bindungspartner bis hin zu polyvalenten Therapeutika aufgezeigt.

Marcus Weber

Papers

Multivalency as a chemical organization and action principle.

Robust Perron cluster analysis in conformation dynamics

Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification

A nontoxic pain killer designed by modeling of pathological receptor conformations

Multivalenz als chemisches Organisations- und Wirkprinzip